Discrete physics using metrized chains

Over the last fifty years, there have been numerous efforts to develop from first principles a comprehensive discrete formulation of geometric physics, including Whitney’s geometric integration theory, Tonti’s work on unification of physical theories, research on mimetic discretization methods, discrete exterior calculus, and Harrison’s theory of chainlets among others. All these approaches strive to separate physical models into standard topological, geometric, and physical components. While each of these components appear to be well understood, the effective computational connection between these three components is still lacking, leading to difficulties in combining, reconciling, and refining physical simulations. This paper proposes such a connection using chains defined on a cell complex, an abstraction of a decomposition of a Riemannian manifold considering only topological-related properties, to establish a discrete metric structure on top of a discrete measure-the...

• Type: Conference
• Year: 2009
• Where: SMA
• Authors: Antonio DiCarlo, Franco Milicchio, Alberto Paoluzzi, Vadim Shapiro
• Keywords: Comprehensive Discrete Formulation, Discrete Metric Structure, Metric Structure, SMA 2009, Solid Modeling